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arXiv · 1309.0572

Diagram automorphisms of quiver varieties

Anthony Henderson·Anthony Licata
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Abstract

We show that the fixed-point subvariety of a Nakajima quiver variety under a diagram automorphism is a disconnected union of quiver varieties for the `split-quotient quiver' introduced by Reiten and Riedtmann. As a special case, quiver varieties of type D arise as the connected components of fixed-point subvarieties of diagram involutions of quiver varieties of type A. In the case where the quiver varieties of type A correspond to small self-dual representations, we show that the diagram involutions coincide with classical involutions of two-row Slodowy varieties. It follows that certain quiver varieties of type D are isomorphic to Slodowy varieties for orthogonal or symplectic Lie algebras.

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BibTeXRIS

Anthony Henderson, Anthony Licata. 2014-09-08. Diagram automorphisms of quiver varieties. https://doi.org/10.1016/j.aim.2014.08.007

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